Author Archives: Raghu Mahajan

About Raghu Mahajan

Postdoctoral research fellow in theoretical physics, studying quantum gravity.

Useful formulas in the canonical ensemble

Posted on January 8, 2019 by Raghu Mahajan

In the canonical ensemble we hold fixed the inverse-temperature . The goal is to compute the partition function . Suppose we find We can compute the entropy One special case is which we get in the case of an extremal … Continue reading →

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Useful formulas in the microcanonical ensemble

Posted on January 8, 2019 by Raghu Mahajan

In the microcanonical ensemble, we fix the energy and ask: What is the entropy as a function of ? Suppose we find a power law, that is, The next step is to compute the temperature We also want to compute … Continue reading →

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Harmonic oscillator partition function using path integrals

Posted on September 11, 2018 by Raghu Mahajan

Two pages of notes explaining how to derive the partition function of the harmonic oscillator using the path integral. Care is needed in normalizing the measure, and relatedly, to deal with the Matsubara zero mode of the free particle. Harmonic … Continue reading →

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Schwarzschild free energy

Posted on September 11, 2018 by Raghu Mahajan

Two pages of notes on computing the Schwarzschild free energy in 4 dimensions, following the 1977 paper of Gibbons and Hawking. Schwarzschild Free Energy

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Videos of some talks I’ve given

Posted on September 5, 2018 by Raghu Mahajan

2015 Kavli Institute, Santa Barbara, California http://online.kitp.ucsb.edu/online/entangled15/mahajan/   2016 Perimeter Institute, Waterloo, Canada http://perimeterinstitute.ca/videos/transport-chern-simons-matter-theories   2018 Kavli Institute, Santa Barbara, California http://online.kitp.ucsb.edu/online/chord18/mahajan/  

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Degree of the identity map on S^2

Posted on August 7, 2018 by Raghu Mahajan

The winding number of the identity map from to  should be one, and we can check this using the following Mathematica code. Denoting the triple product of 3-vectors by square brackets, the general expression is .

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Comparing Sch. black holes with different CC

Posted on July 31, 2018 by Raghu Mahajan

We will restrict to 3+1 dimensions, and compare the emblackening factors.

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Internal spin of a dyon

Posted on July 29, 2018 by Raghu Mahajan

The normalization of gauge fields means that the magnetic charge of the fundamental magnetic monopole is . (It’s magnetic field is , so the flux through the sphere is .) Dirac quantization then tells us that the electric charge is … Continue reading →

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Fibonacci and Ising anyons

Posted on July 29, 2018 by Raghu Mahajan

(This post is very naive, and is only intended to serve as an aid to memory of various facts.) Fibonacci There are two types of anyons: 1 and . The nontrivial fusion rule is . This is as if we … Continue reading →

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Green’s function method with boundary values

Posted on July 24, 2018 by Raghu Mahajan

Let’s keep it simple. Suppose you want to solve the Laplace equation on a domain . The domain has boundary . You are given the source function in the domain , and the boundary condition . The crucial point to … Continue reading →

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